Sanzone is accused of shaking his son, Joshua Millinson, causing fatal head injuries at their Wolverhampton home on October 24 last year.
He is further charged with cruelty to a child and is alleged to have wilfully assaulted Joshua on a separate occasion.
The jury in the trial heard from Natalie Shepherd, who lived at the home in Whitburn Close, Pendeford, with Sanzone, her partner Sharon Howell, and the latter's daughter, Zoe Howell – Joshua's mother.
She recalled two episodes where she believed Sanzone to be alone with Joshua and heard 'bangs.' Asked about the first occasion, she said: "It was a loud bang, like a thump, coming from out of Zoe's and Daniel's bedroom when Daniel was with Joshua in the room.
"Zoe ran in to see what had happened.
"Daniel told her to go back into her mom's room and that he had dropped something on the floor.
"Joshua was 'screaming' crying. That is why Zoe jumped up from our room and ran in."
Miss Shepherd told the jury on a separate occasion she heard a similar 'bang' come from the living room and believed Sanzone was in there with Joshua.
She added Zoe Howell later told her that Sanzone, when questioned, said the noise was the 'remote or something.'
But under cross-examination by Mr David Mason QC, defending Sanzone, she could not remember if she heard a 'bang' on one or two occasions.
The trial has previously heard from Joshua's grandmother Sharon Howell. She told the jury how she desperately fought to revive the baby.
Giving evidence earlier this week, she said: "Zoe came into my room. She said she thought there was something wrong with Joshua and passed him to Natalie.
"Natalie realised something was wrong. Zoe took the baby back and passed him straight to me. That is when I said 'get an ambulance now." She added: "I put my mouth over his. Nothing was happening."
Sanzone, aged 23, denies murdering Joshua, causing or allowing his death and cruelty to a child. Zoe Howell, 19, faces and denies the latter two charges.
Mr Philip Stott, prosecuting, asked Miss Shepherd if she had heard Joshua cry in different ways.
She said: "He would cry if hungry but it was like a screaming cry if his dad had him. It was like he was in pain."
When asked by Mr Mason QC, Miss Shepherd confirmed she had never seen any injury on Joshua.
Joshua was 13-days-old when he was taken to New Cross Hospital in cardiac arrest on October 24.
He died following nearly a month on life support after the High Court ruled his care should be withdrawn.
The trial continues.